Sains Malaysiana 51(11)(2022): 3807-3817
http://doi.org/10.17576/jsm-2022-5111-24
On the
Impact of Asymmetric Dependence in the Actuarial Pricing of Joint Life
Insurance Policies
(Kesan Kebersandaran Asimetri dalam Harga Aktuari Polisi
Insurans Hayat Tercantum)
EMEL
KIZILOK KARA*
Department
of Actuarial Sciences, Faculty of Arts and Sciences, Kirikkale University, Kirikkale,
Turkey
Diserahkan: 1
April 2022/Diterima: 19 Julai 2022
Abstract
Multipopulation
mortality modeling is a significant research problem in actuarial science.
Mortality functions involving multiple lives are also essential to determine
the pricing of premiums. Moreover, the lifetime models based on dependence and
asymmetry are more realistic. Hence, this paper applies an asymmetric copula
model, Generalized FGM (GFGM) to model the bivariate joint distribution of
future lifetimes. Premiums of first-death life insurance products are
calculated based on the proposed model and compared with independent and
symmetrical models. The results display that asymmetry has a significant effect
on premium calculations. Also, it is concluded that the lowest premiums are
generally in asymmetric lifetime models. This paper also provides analytical
examples for the proposed model with Gompertz’s marginal law.
Keywords: Asymmetric dependence;
copula; insurance; joint life (first-death); premium
Abstrak
Pemodelan
mortaliti populasi berbilang merupakan permasalahan penyelidikan yang penting
dalam bidang sains aktuari. Fungsi mortaliti yang melibatkan model hayat
berbilang juga berperanan untuk menentukan harga premium. Selain itu, model
masa-hayat berdasarkan kebersandaran dan asimetri adalah lebih realistik. Oleh
itu, makalah ini menggunakan model kopula asimetri dan Generalized FGM
(GFGM) untuk memodelkan taburan tercantum bivariat bagi jangka hayat masa
hadapan. Premium bagi produk insurans hayat kematian-pertama dihitung
berdasarkan model yang dicadangkan dan dibandingkan dengan model tak bersandar
dan simetri. Keputusan menunjukkan bahawa asimetri mempunyai kesan yang
signifikan ke atas pengiraan premium. Selain itu, dapat disimpulkan bahawa
premium terendah kebiasaannya ditunjukkan dalam model masa hayat asimetri.
Kajian ini juga menyediakan contoh analisis bagi model yang dicadangkan
menggunakan marginal Gompertz.
Kata kunci: Hayat tercantum (kematian-pertama); insurans; kebersandaran asimetri; kopula;
premium
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*Pengarang
untuk surat-menyurat; email: emel.kizilok@kku.edu.tr